By plane

Dubrovnik airport is at 20 km from the city center, and busses from airport and to airport are synchronized with connecting flights.

By bus

From bus station Silos of Trieste (next to the railway station) every day leaves a international bus for Dubrovnik. Busses aren’t always in a good condition, and by them you can reach the city in about 13 hours. During summer holidays, which are characterized by tourists influx, it’s advisable to book the seat at the bus station of Trieste (tel. +39 040 425020 ) and buying the ticket the morning of the departure (it’s not possible to buy the ticket during the days before the departure). It often happens that the bus is full, and so some tourists can’t leave.
A part from this route, there are other routes for Rijeka from which you can catch another bus to reach Dubrovnik.

By car

From Trieste, surpass the ex Pesek/Kozina’s borderline , and go straight on till the Croatia’s borderline where you have to take the highway that arrives nearly Dubrovnik. The alternative is going out from the highway at the junction of Fiume/Rijeka, go straight on the coast road directed to Senj, and before arriving in the city center, take the road on the left following the indications to take the highway which lead to Dubrovnik. Coast road is full of curves and it has only one lane, but it offers a beautiful panorama. The highway is new-built and it has two lanes, except for Sv. Rok gallery (5 km long) and the first part from Rijeka till Dubrovnik.
In case of strong wind, the conjugation from Sv. Rok to Maslinac may be closed to traffic.

By ferry

During summer months ferries leave from Bari every day and reach Dubrovnik’s harbor in 9 hours.

Taken from: wikivoyage